Solve Systems of Equations using Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

Front

What does it mean for a system of equations to have infinite solutions?

Back

A system of equations has infinite solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the equations represent parallel lines that never intersect.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into both equations. If both equations are true, the point is a solution.

Front

What is the first step in using the substitution method?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

Can you provide an example of a system of equations with infinite solutions?

Back

An example is: y = 2x + 3 and 2y = 4x + 6. Both equations represent the same line.

Front

What is the graphical representation of a system of equations with no solution?

Back

The graphical representation is two parallel lines that do not intersect.

Front

What is the solution to the system of equations: 2x + 3y = 12 and x - y = 1?

Back

The solution is (3, 2).

Front

How do you check your solution for a system of equations?

Back

Substitute the solution back into both original equations to verify that both equations hold true.